Optical differential quadrature phase-shift keying (ODQPSK) is an attractive modulation format for high-speed optical communications because it offers high spectral efficiency and high tolerance to chromatic dispersion and polarization-mode dispersion (PMD). An ODQPSK signal is conventionally received by a direct-detection receiver consisting of two optical delay interferometers (ODIs) for demodulation followed by two balanced detectors. While the sensitivity of a direct-detection ODQPSK receiver is better than that of a conventional on-off-keying (OOK) receiver, it is worse than that of a quadrature phase-shift keying (QPSK) receiver with coherent detection. Direct-detection ODQPSK receivers, however, are usually simpler than coherent QPSK receivers.
Optical differential 8-level phase-shift keying (OD8PSK) is another attractive modulation format that offers high spectral efficiency and high tolerance to chromatic dispersion and PMD. The receiver sensitivity of OD8PSK, however, is much worse than that of ODQPSK and optical differential binary phase-shift keying (ODBPSK) for the same data rate. This is because the minimum symbol spacing in the symbol constellation of OD8PSK is much smaller than those of ODBPSK and ODQPK, and the performance of OD8PSK based on differential detection is severely limited by differential phase noise.
There are two common methods that have been used in wireless communications to reduce the performance penalty associated with differential detection: multiple-symbol differential detection (MSDD), and data-aided multi-symbol phase estimation (MSPE). Both the MSDD and MSPE approaches have been extended to optical differential binary phase-shift keying (ODBPSK). For ODQPSK, however, an MSDD receiver would require at least four optical delay interferometers (ODIs) and four balanced detectors, which makes the receiver more complex and potentially expensive. The complexity of an MSDD receiver would be further increased for OD8PSK and optical differential multilevel phase-shift keying signals (ODmPSK) with m>8.